\Mh.dZddlZddlmZgdZedejdd dZedejdd d Zedejdd d Z dS)zTrophic levelsN)not_implemented_for)trophic_levelstrophic_differencestrophic_incoherence_parameter undirectedweight) edge_attrscd|jD}|stjddtj||D}t |t |jkrtjdddl}tj||j }| |d }||dkdd|dkf}|||dkdd|j fz }|j d}| |} |j| |z } n.#|jj$r} d} tj| | d} ~ wwxYw| d d z} i}d |jD}|D]}d ||<d |jD}t#|D]\} }| | ||<|S) aCompute the trophic levels of nodes. The trophic level of a node $i$ is .. math:: s_i = 1 + \frac{1}{k^{in}_i} \sum_{j} a_{ij} s_j where $k^{in}_i$ is the in-degree of i .. math:: k^{in}_i = \sum_{j} a_{ij} and nodes with $k^{in}_i = 0$ have $s_i = 1$ by convention. These are calculated using the method outlined in Levine [1]_. Parameters ---------- G : DiGraph A directed networkx graph Returns ------- nodes : dict Dictionary of nodes with trophic level as the value. References ---------- .. [1] Stephen Levine (1980) J. theor. Biol. 83, 195-207 c$g|] \}}|dk |S)r).0ndegs f/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/networkx/algorithms/centrality/trophic.py z"trophic_levels..-s!;;;C#((1(((z|This graph has no basal nodes (nodes with no incoming edges).Trophic levels are not defined without at least one basal node.ch|] }|D]}| Sr r )r layernodes r z!trophic_levels..4s9EDHr)sourceszTrophic levels are only defined for graphs where every node has a path from a basal node (basal nodes are nodes with no incoming edges).rNr)axisc3,K|]\}}|dk |VdSrNr r node_iddegrees r z!trophic_levels..[s*OO&6Q;;W;;;;OOrc3,K|]\}}|dk |VdSrr rs rr z!trophic_levels..`s+RROGVfPQkkkkkkRRr) in_degreenx NetworkXError bfs_layerslennodesnumpyadjacency_matrixTtoarraysumnewaxisshapeeyelinalginv LinAlgError enumerateitem)Gr basal_nodesreachable_nodesnparowsumpnnirerrmsgylevels zero_node_idsrnonzero_node_idss rrr sHH<;1;;;;K   N   -;???O ?s17||++ P    Af---/7799AVVAAV  F &A+qqq&A+~&A F6Q; 2: ..A B r A - IMM!a%  9 --- ) s##,- 1 A FPOAKOOOM wSRq{RRR 011$$ 7&&))w Ms$EE-E((E-crt||}i}|jD]\}}||||z |||f<|S)asCompute the trophic differences of the edges of a directed graph. The trophic difference $x_ij$ for each edge is defined in Johnson et al. [1]_ as: .. math:: x_ij = s_j - s_i Where $s_i$ is the trophic level of node $i$. Parameters ---------- G : DiGraph A directed networkx graph Returns ------- diffs : dict Dictionary of edges with trophic differences as the value. References ---------- .. [1] Samuel Johnson, Virginia Dominguez-Garcia, Luca Donetti, Miguel A. Munoz (2014) PNAS "Trophic coherence determines food-web stability" r)redges)r5rrAdiffsuvs rrrgsQ8Af - - -F E..1q F1I-q!f LrFctddl}|rt||}n`ttj|}|r*|}||n|}t||}t|t| S)a+Compute the trophic incoherence parameter of a graph. Trophic coherence is defined as the homogeneity of the distribution of trophic distances: the more similar, the more coherent. This is measured by the standard deviation of the trophic differences and referred to as the trophic incoherence parameter $q$ by [1]. Parameters ---------- G : DiGraph A directed networkx graph cannibalism: Boolean If set to False, self edges are not considered in the calculation Returns ------- trophic_incoherence_parameter : float The trophic coherence of a graph References ---------- .. [1] Samuel Johnson, Virginia Dominguez-Garcia, Luca Donetti, Miguel A. Munoz (2014) PNAS "Trophic coherence determines food-web stability" rNr) r(rlistr#selfloop_edgescopyremove_edges_fromfloatstdvalues)r5r cannibalismr8rF self_loopsG_2s rrrs8 8#Af555"+A..//  &&((C  ! !* - - - -C#C777 U\\^^,,-- . ..rr)rF) __doc__networkxr#networkx.utilsr__all__ _dispatchablerrrr rrrYs...... T T T\""X&&&YYY'&#"Yx\""X&&&'&#"B\""X&&&)/)/)/'&#")/)/)/r